Long-range correlations in a locally driven exclusion process

Tridib Sadhu (1) , Satya N. Majumdar (2) , David Mukamel (3)

1 IPHT - Institut de Physique Théorique - UMR CNRS 3681
2 LPTMS - Laboratoire de Physique Théorique et Modèles Statistiques
3 Weizmann Institute

We show that the presence of a driven bond in an otherwise diffusive lattice gas with simple exclusion interaction results in long-range density-density correlation in its stationary state. In dimensions $d>1$ we show that in the thermodynamic limit this correlation decays as $C(r,s)\sim (r^2+s^2)^{-d}$ at large distances $r$ and $s$ away from the drive with $|r-s|>>1$. This is derived using an electrostatic analogy whereby $C(r,s)$ is expressed as the potential due to a configuration of electrostatic charges distributed in $2d$-dimension. At bulk density $\rho=1/2$ we show that the potential is that of a localized quadrupolar charge. At other densities the same is correct in leading order in the strength of the drive and is argued numerically to be valid at higher orders.

Domaines: Mécanique statistique [cond-mat.stat-mech]

Tridib Sadhu, Satya N. Majumdar, David Mukamel. Long-range correlations in a locally driven exclusion process. Physical Review E : Statistical, Nonlinear, and Soft Matter Physics, 2014, 90 (1), pp.012109. ⟨10.1103/PhysRevE.90.012109⟩. ⟨hal-01053571⟩